539.3

interphase insection, isotropic plate, reinforcing rib, contact forces, singular integral equations, smooth contact area.

In the conditions of the general flat stress state created by uniformly distributed effects of tension (compression) at infinity, the mixed contact problem for an infinite isotropic plate with a circular hole, which contour reinforced by a closed elastic rib in the presence of a symmetrical interfacial section at the boundary of their connection and the edges of cut in the process of deformation is smoothly contacted, is considered. The components of the deformation tensor (unit elongation, the angle of rotation of the normal and the curvature) at the point of the contour of the hole of the plate are represented by integral dependences on the contact forces. By modeling the reinforcement of a closed elastic rod of a stable rectangular cross of large curvature and using the basic equations of linear theory of curvilinear rods the mathematical model of problems is constructed in the form of systems of three singular integral equations with Hilbert cores to find contact forces between plates and rib. To determine the initial parameters of a closed static indeterminate rod, the conditions of unambiguous displacement and angles of rotation at the point of its axis and the equilibrium conditions are used. The approximate solution of the problem is constructed by the method of mechanical quadrature and collocations, which investigated the influence on the stress state of the plate and the reinforcing rib and on the size of the area of smooth contact of stiffness factor of rib.

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1. Sulym H. T. Osnovy matematychnoi teorii termopruzhnoi rivnovahy deformivnykh tverdykh til z tonkymy vkliuchenniamy: monohrafiia. Lviv, Doslidno-vydavnychyi tsentr NTSh, 2007. 715 p. [In Ukrainian].
2. Bozhydarnik V. V., Andreikiv O. E., Sulym H. T. Mekhanika ruinuvannia, mitsnist i dovhovichnist neperervno armovanykh kompozytiv: monohrafiia. In 2 Vol. Vol. 2. Matematychni metody v zadachakh mekhaniky ruinuvannia neperervno armovanykh kompozytiv. Lutsk: Nadstyria, 2007. 424 p. [In Ukrainian].
3. Shvabiuk V. I. Opir materialiv: pidruchnyk. Kiev: Znannia, 2016. 407 p. [In Ukrainian].
4. Siaskyi A., Shevtsova N. Zastosuvannia metodu syl dlia statychnoho rozrakhunku zamknenykh kryvoliniinykh stryzhniv. Visnyk TNTU. 2015. No. 3 (79). P. 24–30. [In Ukrainian].
5. Deineka O. Yu. Rozrakhunok plastynchastykh elementiv konstruktsii z kryvoliniinymy rebramy zhorstkosti za naiavnosti mizhfaznykh rozriziv. Dys. kand. tekhn. nauk: 01.02.04. Lutsk, 2021. 140 p. [In Ukrainian].
6. Hovorukha V. B., Loboda V. V. Modeli ta metody ruinuvannia piezokeramichnykh til z mizhfaznymy trishchynamy. Dnipro: Vyd-vo Dnipropetr. un-tu, 2013. 252 p. [In Ukrainian].
7. Martyniak R. M., Serednytska Kh. I. Kontaktni zadachi termopruzhnosti dlia mizhfaznykh trishchyn v bimaterialnykh tilakh. Lviv: Rastr-7, 2017. 168 p. [In Ukrainian].
8. Hodes A. Yu., Loboda V. V. Duhova trishchyna v odnoridnomu elektrostryktsiinomu materiali. Matematychni metody i fizyko-mekhanichni polia. 2015. No. 4 (58). P. 90–102. [In Ukrainian].
9. Ostryk V. I. Kontakt berehiv mizhfaznoi napivneskinchennoi trishchyny. Matematychni metody i fizyko-mekhanichni polia. 2020. No. 1 (63). P.106–121. [In Ukrainian].
10. Kaminskyi A. O., Selivanov M. F., Chornoivan Yu. O. Vyznachennia kontaktnykh napruzhen mizh berehamy trishchyny normalnoho vidryvu. Dop. NAN Ukrainy. 2016. No. 5. P. 36–42. [In Ukrainian].
11. Chumak K., Malanchuk N., Martynyak R. Partial slip contact problem for solids with regular surface texture assuming thermal insulation or thermal permeability of interface gaps (review) Int. J. Mech. Sci. 2014. No. 84. P.138–146.
12. Siaskyi A. O., Shevtsova N. V., Deineka O. Yu. Mizhfaznyi rozriz v ortotropnii plastyntsi z pidsylenym kruhovym konturom. Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky. 2018. No. 5.
    P. 176–181. [In Ukrainian]